Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: ers, regardless of how weird that subset may be, can be the domain of a function. As our exploration of functions continued beyond Section 1.4, we saw fewer and fewer functions with ‘weird’ domains. It is worth your time to go back through the text to see that the domains of the polynomial, rational, exponential, logarithmic and algebraic functions discussed thus far have fairly predictable domains which almost always consist of just a collection of intervals on the real line. This may lead some readers to believe that the only important functions in a College Algebra text have domains which consist of intervals and everything else was just introductory nonsense. In this section, we introduce sequences which are an important class of functions whose domains are the set of natural numbers.1 Before we get to far ahead of ourselves, let’s look at what the term ‘sequence’ means mathematically. Informally, we can think of a sequence as an inﬁnite list of numbers. For example, consider the sequence 1 3 9 27 ,− , ,− ,... 2 4 8 16 (1) As usual, the periods of...
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